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Multinomial Logistic Regression Tool

Design prototype

Explore multinomial logistic regression for marketing outcomes with more than two categories (for example, multi-level brand choice or multi-step funnel stage). Upload raw data, select the outcome and predictors, and compare predicted class probabilities with diagnostics.

TEST OVERVIEW & EQUATIONS

Multinomial logistic regression is used when the outcome has more than two unordered categories (for example, Brand A / Brand B / Brand C or aware / considering / ready to buy). It models how a set of predictors changes the probability of landing in each category, relative to a chosen reference outcome.

For each non-reference outcome category \(j\), the model estimates a separate log-odds equation relative to the reference category \(\text{ref}\):

$$ \log \frac{P(Y = j)}{P(Y = \text{ref})} = \beta_{0j} + \beta_{1j} x_1 + \cdots + \beta_{pj} x_p,\quad j = 1, \ldots, K - 1. $$

These log-odds are converted into predicted probabilities using the multinomial logistic (softmax) link:

$$ P(Y = j) = \frac{\exp(\eta_j)}{1 + \sum_{h \neq \text{ref}} \exp(\eta_h)},\quad P(Y = \text{ref}) = \frac{1}{1 + \sum_{h \neq \text{ref}} \exp(\eta_h)} $$ where \(\eta_j = \beta_{0j} + \beta_{1j} x_1 + \cdots + \beta_{pj} x_p\).

Additional Notes / Formulas

Choosing the reference outcome category changes the interpretation of coefficients but not the underlying probabilities. A positive coefficient \(\beta_{kj}\) means that as predictor \(x_k\) increases, outcome \(j\) becomes more likely relative to the reference category, holding other predictors constant.

MARKETING SCENARIOS

Use presets to auto-load realistic marketing inputs, text, and any CSV/TSV data required for uploads. The download button exposes the exact dataset used so editors can tweak it in Excel or Numbers before re-uploading.

INPUTS & SETTINGS

Upload data

Upload raw long-format data

The template shows group,value,channel,note columns so end users can include the outcome plus optional metadata (channel, creative, timestamp). Customize those columns to the raw format your tool expects, and call out when only two group labels are allowed.

Drag & drop raw case file

Two columns minimum: group label and numeric metric.

No raw file uploaded.

Outcome & Reference Category

Choose the multinomial outcome (with 2 or more categories) and which outcome level should serve as the reference (baseline) category in the model. Coefficients and probability plots will be interpreted relative to this reference outcome.

Select predictors

Check the box for each predictor you want to include in the model. For categorical predictors, the app will create one coefficient per non-reference category. For continuous predictors, the app will estimate a single slope per outcome contrast.

Standardization affects model fitting and effect plots only. Summary statistics always report predictors on their original scale.

Analysis Settings

Advanced analysis settings

Adjust optimization settings for the multinomial model. Defaults are suitable for most datasets; increase the maximum iterations or decrease the step size if convergence warnings appear.

Higher max iterations (up to 50,000) can improve convergence for difficult models but will increase run time.

VISUAL OUTPUT

Predicted probabilities vs. focal predictor

Focal range (continuous):

Hold other predictors constant

Choose levels/values for the non-focal predictors used when plotting the focal curve.

After you upload data, choose an outcome, select at least one predictor (with at least one continuous predictor to see the line view), and run the model, this chart will show how the predicted probability of each outcome changes with the focal predictor while holding others constant.

Interpretation Aid

The line (or bars for categorical focals) shows the predicted probability of each outcome category while holding other predictors constant at chosen values. Steeper slopes or larger gaps between bars imply stronger effects. Confidence bands/bars reflect the statistical uncertainty for those probabilities; wider bands mean less certainty. If bands for different categories overlap heavily, the model may not distinguish them well at those settings.

Observed vs predicted outcome distribution

This bar chart compares how often each outcome category appears in the modeled data (observed) with the predicted class counts (hard classification by highest predicted probability). Use the controls below to switch between counts and percentages or to hide the predicted bars.

Interpretation Aid

Observed bars show the actual distribution. Predicted bars come from assigning each row to the outcome with the highest predicted probability, so counts are integer (or proportions if you toggle percentage view). Large gaps suggest misfit or missing predictors; close alignment means the model’s classifications mirror the observed mix.

Visual Output Settings

SUMMARY STATISTICS

Summary Statistics

Continuous Predictors

Variable Mean Median Std. Dev. Min Max
Provide data to see summary statistics.

Categorical Predictors (% by level)

Predictor Level Percent
Provide data to see level percentages.

TEST RESULTS

Regression Equation

Show regression equations

Run the model to view the fitted log-odds equations for each outcome contrast.

Model log-likelihood: –
Approx. degrees of freedom: –
p-value (not computed): –
Pseudo-R² (McFadden): –
Interpretation Aid

Log-likelihood: Higher (less negative) is better fit; values are comparable only across models on the same data.

Degrees of freedom: Rough count of free parameters ((K-1) × predictors); larger models risk overfitting with small samples.

Pseudo-R²: McFadden’s measure of improvement over a null model; use for relative comparison, not literal percent variance explained.

APA-Style Report

Placeholder APA narrative will appear here.

Managerial Interpretation

Business-focused copy referencing scenario inputs appears here.

Coefficient Table (log-odds relative to reference outcome)

Outcome contrast Predictor term Coefficient (log-odds) Std. Error p-value 95% CI
Run the model to view coefficients for each outcome category relative to the reference.
Interpretation Aid
Coefficients are log-odds relative to the reference outcome. Exponentiating a coefficient gives an odds ratio for that contrast. Large standard errors or very wide CIs indicate unstable estimates (often due to sparse categories or collinearity).

This download exports the original uploaded data plus one column for the most likely outcome category and one column per outcome with its predicted probability from the fitted multinomial model.

DIAGNOSTICS & ASSUMPTIONS

Diagnostics & Assumption Tests

Explain assumption checks (sample size, variance, normality, expected counts, leverage points). Populate via JS.